Simplify the following expression: $\dfrac{36t}{72t^3}$ You can assume $t \neq 0$.
Answer: $ \dfrac{36t}{72t^3} = \dfrac{36}{72} \cdot \dfrac{t}{t^3} $ To simplify $\frac{36}{72}$ , find the greatest common factor (GCD) of $36$ and $72$ $36 = 2 \cdot 2 \cdot 3 \cdot 3$ $72 = 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3$ $ \mbox{GCD}(36, 72) = 2 \cdot 2 \cdot 3 \cdot 3 = 36 $ $ \dfrac{36}{72} \cdot \dfrac{t}{t^3} = \dfrac{36 \cdot 1}{36 \cdot 2} \cdot \dfrac{t}{t^3} $ $\phantom{ \dfrac{36}{72} \cdot \dfrac{1}{3}} = \dfrac{1}{2} \cdot \dfrac{t}{t^3} $ $ \dfrac{t}{t^3} = \dfrac{t}{t \cdot t \cdot t} = \dfrac{1}{t^2} $ $ \dfrac{1}{2} \cdot \dfrac{1}{t^2} = \dfrac{1}{2t^2} $